I have done this before on GoDaddy without a hitch, but I cannot seem to figure out this particular case.

I have a domain space with temporary URL http://yogainun.mysubname.com and am hosting the domain name that is to be applied to it at 1und1.de. Right now I have set it up so that from the 1und1 domain name hosting the address http://www.yoga-in-unternehmen.de is frame redirected to the subdomain that I just referred to.

But this is not what I want.

http://www.yoga-in-unternehmen.de is to be the domain. With the frame redirect, URL's like http://www.yoga-in-unternehmen.de/example-article do not show up. But this is what I want.

With GoDaddy in a similar case, I just turned on DNS and changed the name servers. That worked without problem, but with 1und1 not. Is there something I am missing?

Currently, you seem to have two domains: yoga-in-unternehmen.de with DNS and website hosted by 1&1, and yogainunternehmen.de hosted by some other host. The first domain currently only returns a frameset that loads the actual content from the second host.

As you correctly note, this is not a very good arrangement. (I won't enumerate the reasons here — it should suffice to note that there are very few problems for which HTML frames are the correct solution.) What is the correct answer depends on just what you want to achieve, and what features your hosting providers support:

If you want to keep the actual content hosted at yogainunternehmen.de, but have yoga-in-unternehmen.de be the domain seen by users, one solution is to add a CNAME DNS record from yoga-in-unternehmen.de (and www.yoga-in-unternehmen.de) to yogainunternehmen.de.

If the hosting provider for yogainunternehmen.de is using name-based virtual hosting (which they most likely are), you'll also need to let them know that yoga-in-unternehmen.de is now an alias for yogainunternehmen.de. (In fact, you should do this first, before adding the CNAME record.) This may be possible from their control panel, or you may need to contact them personally.

Finally, you should add a HTTP 301 redirect from yogainunternehmen.de to yoga-in-unternehmen.de, so that you won't be serving duplicate content from the two domains. As the websites for both domains are now served from the same host, you can do this entirely there. Some hosting providers may let you do this entirely from their control panel; otherwise, if you have (or can add) an .htaccess file in your website root directory for yogainunternehmen.de (which is also now serving yoga-in-unternehmen.de), and the webserver supports mod_rewrite, you can use the following ruleset:

Alternatively, instead of using CNAME, you could just move both domains to the same DNS and web hosting provider (it doesn't even have to be either of your current providers), and have them configure them as aliases of each other. This might be cheaper than maintaining two separate hosting accounts. For the practical details of arranging that, I'd suggest asking the hosting provider you want to move to — they'll have a financial incentive to help you as much as possible. You will still most likely want to retain both domains, and have one serve 301 redirects to the other, just so that you won't break any existing links to your site and won't lose any search engine rank.